Related papers: A parallel edge orientation algorithm for quadrila…
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…
Shape assembly composes complex shapes geometries by arranging simple part geometries and has wide applications in autonomous robotic assembly and CAD modeling. Existing works focus on geometry reasoning and neglect the actual physical…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…
The problem of identifying intersections between two sets of d-dimensional axis-parallel rectangles appears frequently in the context of agent-based simulation studies. For this reason, the High Level Architecture (HLA) specification -- a…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
We present a particle locating method for unstructured meshes in two and three dimensions. Our algorithm is based on a patch searching process, and includes two steps. We first locate the given point to a patch near a vertex, and then the…
This paper presents a novel algorithmic framework for the computational design, simulation, and fabrication of a hexagonal grid-based double-curvature structure with planar hexagonal panels. The journey begins with constructing a robust…
We present two parallel optimization algorithms for a convex function $f$. The first algorithm optimizes over linear inequality constraints in a Hilbert space, $\mathbb H$, and the second over a non convex polyhedron in $\mathbb R^n$. The…
Many important applications across science, data analytics, and AI workloads depend on distributed matrix multiplication. Prior work has developed a large array of algorithms suitable for different problem sizes and partitionings including…
A new approach for the parallel forward modeling of transient electromagnetic (TEM) fields is presented. It is based on a family of uniform-in-time rational approximants to the matrix exponential that share a common denominator independent…
Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf…
We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimentional case in certain discrete…
We consider the problem of minimizing a function over the manifold of orthogonal matrices. The majority of algorithms for this problem compute a direction in the tangent space, and then use a retraction to move in that direction while…
Mesh generation plays a crucial role in scientific computing. Traditional mesh generation methods, such as TFI and PDE-based methods, often struggle to achieve a balance between efficiency and mesh quality. To address this challenge,…
A low out-degree orientation directs each edge of an undirected graph with the goal of minimizing the maximum out-degree of a vertex. In the parallel batch-dynamic setting, one can insert or delete batches of edges, and the goal is to…
Current successful approaches for generic (non-semantic) segmentation rely mostly on edge detection and have leveraged the strengths of deep learning mainly by improving the edge detection stage in the algorithmic pipeline. This is in…